Simplify Square Root of 83129

What is the square root of 83129 in its simplest radical form? To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√83129 = A√B

Unfortunately, the square root of 83129 cannot be simplified. Thus, here is the answer to the square root of 83129 in its simplest form:

√ 83129 = √ 83129

Here are two different methods we used to determine why the square root of 83129 cannot be simplified.

1) To be able to simplify the square root of 83129, one of the factors of 83129 other than 1 must be a perfect square. The factors of 83129 are 1, 97, 857, and 83129. Since none of these factors are perfect squares, the square root of 83129 cannot be simplified.

2) To be able to simplify the square root of 83129, all the prime factors of 83129 cannot be unique. When we did prime factorization of 83129, we found that 97 x 857 equals 83129. Since all the prime factors are unique, the square root of 83129 cannot be simplified.

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